Hey, thanks for that wonderful feed-back!

Ok, so let's take it on turns.
1. Well, usually it was seen throughout the manga that when it's one of theirs, they don't talk that formal. Even if she wouldn't know her real name at least they would've called it by the known spy name. We have that example with Yamato actually being Tenzou but people always referred to him in a more familiar way, even if they called him by his code name.
But you are right as well. Though I really tend to believe she was not a spy, though at the beginning I inclined to think the same.
2. That is true, nevertheless. But the whole context here made me believe that is something special about her. I think it might be related to her medical nin abilities... I mean, she was a medic nin at the age of 12? That's pretty impressive. We never saw such a young medic nin except, Tsunade, of course, who graduated Academy at 6. And maybe it was somehow a trap to make her take Kakashi's eye. That's why I came with the theory of Danzo's involvement. Still not sure about everything though as it's foggy but your point is valid as well.
As I said, the whole context made me think she was not a Mist spy. Other countries did the same when it came to the a dead comrade, took its bodies in order for the other countries to not unveil the secret its body had, especially when it came to doujutsus.
3. As I said, here I introduced Danzo's involvement. He was known for wanting to collect sharingans. And maybe that's why he wanted to have Shisui's eye because he couldn't have Kakashi's one in the first place.
Plus, from all the other signs, the only one that matches, is Konoha's. Now if they were all or not, we can't be certain. That's where the mistery is placed. And regarding the masks, well, they are easy to get as we've seen that basical ANBU ones are taken from regular shops, lol.
4. I based that theory by the extreme change it took place on the scenario and the fact that Obito for a moment didn't knew where he was and on the fact that being his dimension he could change it however he wanted, just like genjutsu does, only that genjutsu is an illusion, Kamui dimension is something a bit different, but the base principle would be the same. Not 100% about it though, that's why it's just a theory.
Hmm, you theory about Danzo could add, indeed... And regarding Kakashi, maybe he got the whole package too late, when he was already worn out... Dunno what to say, those are the missing puzzles.
Anyway, thanks for the great feed-back!